Enhancement of seismic data

ABSTRACT

Methods, systems, and computer-readable medium to perform operations including: generating a first time-frequency spectrum of a first seismic trace from an original seismic dataset; generating a second time-frequency spectrum of a second seismic trace from an enhanced seismic dataset, where the second seismic trace corresponds to the first seismic trace; and re-combining an amplitude spectrum of the first time-frequency spectrum and a phase spectrum of the second time-frequency spectrum to generate a third time-frequency spectrum of an output trace that corresponds to the first and second seismic traces.

TECHNICAL FIELD

This disclosure relates to exploration seismology and, morespecifically, to seismic data processing.

BACKGROUND

Seismic data is obtained from seismic surveys to image geologicalstructures of a subterranean region. In particular, seismic data is usedto identify geologic structural and stratigraphic features, such assubsurface faults and unconformities. Poststack seismic data can includetwo-dimensional (2D) seismic slices or three-dimensional (3D) seismicvolumes. Prestack seismic data can have higher dimensions, includingsource and receiver positions arranged in orthogonal directions.

SUMMARY

The present disclosure describes seismic processing methods forpreserving high-frequency content in seismic data that has undergonesignal-to-noise ratio (SNR) enhancement. SNR enhancement procedures,such as nonlinear beamforming (NLBF) and supergrouping (SG), performlocal stacking of prestack seismic data that includes weak orindecipherable seismic signals. While SNR enhancement procedures improveprestack data, it does so at the expense of damaging higher frequenciesin the seismic data. Damaging higher frequencies in the seismic datareduces the frequency band of the prestack data and leads to loss ofvertical resolution in the prestack data.

Aspects of the subject matter described in this specification may beembodied in methods that include the actions of: generating a firsttime-frequency spectrum of a first seismic trace from an originalseismic dataset; generating a second time-frequency spectrum of a secondseismic trace from an enhanced seismic dataset, where the second seismictrace corresponds to the first seismic trace; and re-combining anamplitude spectrum of the first time-frequency spectrum and a phasespectrum of the second time-frequency spectrum to generate a thirdtime-frequency spectrum of an output trace that corresponds to the firstand second seismic traces.

The previously-described implementation is implementable using acomputer-implemented method; a non-transitory, computer-readable mediumstoring computer-readable instructions to perform thecomputer-implemented method; and a computer system comprising a computermemory interoperably coupled with a hardware processor configured toperform the computer-implemented method or the instructions stored onthe non-transitory, computer-readable medium. These and otherembodiments may each optionally include one or more of the followingfeatures.

In a first aspect, generating a time-based output trace from the thirdtime-frequency spectrum.

In a second aspect, where generating the first time-frequency spectrumincludes using short-term Fourier transform (STFT) to generate the firsttime-frequency spectrum, and wherein generating the time-based outputtrace includes using inverse short-term Fourier transform (ISTFT) togenerate the time-based output trace.

In a third aspect, where the enhanced seismic dataset is generated byperforming a signal-to-noise ratio (SNR) enhancement procedure on theoriginal seismic dataset.

In a fourth aspect, where the SNR enhancement procedure includes:common-reflection surface method (CRS), multi-focusing (MF),supergrouping, or non-linear beamforming.

In a fifth aspect, where the enhanced seismic dataset has an identicalacquisition geometry to the original seismic dataset, and where thesecond seismic trace is located in the same position in the enhancedseismic dataset as the first seismic trace in the original seismicdataset.

In a sixth aspect, where the original seismic dataset includes aplurality of seismic traces, and for each seismic trace of theplurality, generating a respective output trace corresponding to theseismic trace, where the respective output traces collectively form anoutput seismic dataset.

The subject matter described in this disclosure can be implemented torealize one or more of the following advantages. The described subjectmatter can achieve a wider frequency band (particularly in thehigher-frequency region) for prestack seismic data that has undergoneSNR enhancement. Maintaining high frequency content in seismic dataallows for more resolved seismic images (in time or depth) and detectionof finer structures in the subsurface than is possible by seismic datain which the high frequency content is suppressed. Furthermore, thedescribed subject matter is computationally effective, and thus, may beused to process modern high-channel count seismic datasets. Otheradvantages will be apparent to those of ordinary skill in the art.

The details of one or more implementations of the subject matter of thisdisclosure are set forth in the description, the claims, and theaccompanying drawings. Other features, aspects, and advantages of thesubject matter will become apparent from the description, the claims,and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flowchart of a first example seismic processing method,according to some implementations of the present disclosure.

FIG. 2 is a flowchart of a second example seismic processing method,according to some implementations of the present disclosure.

FIG. 3 is a flowchart of a third example seismic processing method,according to some implementations of the present disclosure.

FIGS. 4A, 4B, 4C, and 4D illustrate an example of a seismic processingmethod applied to a seismic trace, according to some implementations ofthe present disclosure.

FIGS. 5A, 5B, 5C, 5D, and 5E illustrate examples of seismic processingmethods applied to a seismic dataset, according to some implementationsof the present disclosure.

FIGS. 6A and 6B each illustrate a comparison of averaged amplitudespectra of an original dataset, an enhanced dataset, and outputdatasets, according to some implementations of the present disclosure.

FIGS. 7A, 7B, and 7C illustrate an original dataset stack, an enhanceddataset stack, and an output dataset stack, according to someimplementations of the present disclosure.

FIG. 8 illustrates a comparison of averaged amplitude spectra of anoriginal dataset stack, an enhanced dataset stack, and an output datasetstack, according to some implementations of the present disclosure.

FIG. 9 illustrates an example seismic survey, according to someimplementations of the present disclosure.

FIG. 10 is a block diagram of an example computer system used to providecomputational functionalities associated with described algorithms,methods, functions, processes, flows, and procedures, according to someimplementations of the present disclosure.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

The following detailed description describes methods and systems forpreserving high-frequency content in prestack seismic data that hasundergone signal-to-noise ratio (SNR) enhancement. Variousmodifications, alterations, and permutations of the disclosedimplementations can be made and will be readily apparent to those ofordinary skill in the art. Further, the general principles defined maybe applied to other implementations and applications, without departingfrom the scope of the disclosure. In some instances, details unnecessaryto obtain an understanding of the described subject matter may beomitted so as to not obscure one or more described implementations withunnecessary detail since such details are within the skill of one ofordinary skill in the art. The present disclosure is not intended to belimited to the described or illustrated implementations. Furthermore,the present disclosure is to be accorded the widest scope consistentwith the described principles and features.

I. Overview

Traditionally, land seismic data acquisitions have been performed withfield arrays that include a number of geophones on the order of high 10sto low 100s (for example, 72 geophones or more). In recent practice,however, many land seismic data acquisitions are performed with smallfield arrays (that is, smaller than traditional field arrays) thatinclude a number of geophones-per-channel on the order of low 10s oreven in the single digits (for example, 15 geophones or less).

However, using smaller field arrays is detrimental to the SNR of theseismic datasets that is acquired by the smaller field arrays.Additionally, processing prestack data in these seismic datasets ischallenging because the signals (for example, reflections) are masked bynoise. For instance, it is challenging and unreliable to applyconventional time processing algorithms to this prestack data becausethe derived processing parameters are based on noise. In order toimprove the reliability and utility of seismic datasets that areacquired by small field arrays, the noise in the prestack data needs tobe suppressed and the signals need to be enhanced.

Several existing enhancement procedures are used to enhance prestackdata. These procedures, which are generally referred to as SNRenhancement procedures, include multi-dimensional data-driven stackingtechniques, such as the common-reflection surface method (CRS) andmulti-focusing (MF). These techniques have also been adopted fortwo-dimensional (2D) and three-dimensional (3D) cases in a procedurecalled non-linear beamforming (NLBF). The common feature amongst theseprocedures is the local stacking of coherent signals registered byneighboring traces. To obtain reliable signals from noisy data, SNRenhancement procedures require large stacking apertures that can reachhundreds of meters. Furthermore, the procedures require several hundred(or even thousands) of traces to produce an output trace with anincreased SNR that is acceptable for processing.

Individual traces within such large sets are usually recorded underdifferent near-surface conditions. As a result, the traces have moderateor severe local waveform variations. Consequently, the enhanced data(that is, the output of the SNR enhancement procedures) suffers fromsuboptimal stacking, which results in the suppression of high-frequencycontent of the signals within the traces. The suppression ofhigh-frequency content is an undesirable side effect of multi-channeldata enhancement procedures. Maintaining high-frequency content inseismic data is important for producing more resolved seismic images (intime or depth) and detecting finer structures in the subsurface.

This disclosure describes seismic processing methods for preservinghigh-frequency content in seismic data that has undergone SNRenhancement. In this disclosure, “original” seismic data that hasundergone SNR enhancement is also referred to as “enhanced” data orenhanced traces. Furthermore, for typical surface broadband seismicacquisition, when the sweep signal of sources varies in the interval2-120 Hertz (Hz), “high-frequency” means a range of frequencies of˜40-120 Hz.

In an embodiment, the disclosed seismic processing methods use theoriginal and enhanced traces as building blocks to construct outputtraces that preserve high-frequency content. Since seismic traces arenon-stationary, the original and enhanced traces are decomposed into thetime-frequency (TF) domain using short-time Fourier transform (STFT). Inthe TF domain, the output traces are constructed using the TF spectra ofthe original and enhanced traces. Once generated in the TF domain, theoutput traces are synthesized into the time domain using inverseshort-time Fourier transform (ISTFT).

II. Methods and Systems for Preserving High-Frequency Content in SeismicData that has Undergone SNR Enhancement

The disclosed seismic processing methods serve as an extension of SNRenhancement procedures. Specifically, the disclosed seismic processingmethods can be applied after an enhanced dataset is generated using anSNR enhancement procedure. The process of generating an output datasetthat improves the SNR of the original dataset and that preserveshigh-frequency content is a two-step process. In the first step, an SNRenhancement procedure generates an enhanced seismic dataset thatimproves the SNR of the original dataset. In the second step, one of thedisclosed seismic processing methods uses the original and enhanceddatasets to construct the output dataset that effectively restores thehigh-frequency content lost during the SNR enhancement procedure.

For the purposes of this disclosure, the following assumptions are madeabout the original and enhanced datasets. First, the original datasethas passed through a standard seismic signal processing workflow thatincludes processes such as noise removal, static correction, anddeconvolution. Second, the enhanced dataset has improved SNR incomparison to the original dataset. Third, the high-frequency content ofthe enhanced dataset is suppressed because of suboptimal stacking duringthe SNR enhancement procedure. Fourth, the enhanced dataset retains thesame acquisition geometry as the original dataset (that is, the seismictraces in the enhanced dataset are located in the same positions as inthe original dataset). As such, a j-th trace in the original datasetcorresponds to a j-th trace in the enhanced dataset, where the j-thenhanced trace is an SNR enhanced version of the j-th original trace.

In the first step of generating the output dataset, an SNR enhancementprocedure generates the enhanced dataset based on the original dataset.In this process, weak reflections in the seismic data are identified andinterpreted to generate an enhanced dataset. In particular, the enhanceddataset is constructed using local traveltime information about desiredarrivals. Each trace of the enhanced dataset is constructed by stackingof neighboring traces of original (noisy) dataset along specificallydetermined trajectories within predefined apertures. These trajectoriesdescribe time delays of corresponding arrivals of reflected waves insome vicinity of an enhanced trace. This is considered delay-and-sumbeamforming. Details of SNR enhancement procedures are disclosed inPCT/RU2018/000079, titled “Systems and Methods to Enhance 3-D PrestackSeismic Data Based on Non-Linear Beamforming in the Cross-SpreadDomain,” which is incorporated by reference.

Generally, the SNR enhancement procedure suppresses a noise component inthe original dataset to generate the enhanced dataset, thereby improvingthe SNR. As such, the original dataset can be defined as the sum of theenhanced dataset and the suppressed noise component:

x _(j)(t)=s _(j)(t)+n _(j)(t).  (1)

In equation (1), x_(j)(t) is a j-th trace from the original dataset(also referred to as Trace1), s_(j)(t) is a corresponding j-th tracefrom the enhanced dataset (also referred to as Trace2), and n_(j)(t) isa “noise” component of Trace1 that has been suppressed by the SNRenhancement procedure (that is, the j-th noise component in the originaldataset).

From equation (1), the noise component of Trace1 is defined as shown inequation (2):

n _(j)(t)=x _(j)(t)−s _(j)(t).  (2)

The term n_(j)(t) includes both random and coherent noise that has beensuppressed in s_(j)(t) by the SNR enhancement procedure. However, due tosuboptimal stacking during the SNR enhancement procedure, n_(j)(t) alsoincludes a residual component of the signal (from the original trace)that has been suppressed by the SNR enhancement procedure. Accordingly,n_(j)(t) is also defined as the sum of the actual noise component andthe suppressed residual component of the signal:

n _(j)(t)={circumflex over (n)} _(j)(t)+δs _(j)(t).  (3)

In equation (3), {circumflex over (n)}_(j)(t) is the j-th actual noisecomponent and δs_(j)(t) is the suppressed residual component of the j-thsignal.

In order to improve the enhanced dataset, the suppressed residualcomponent of the signal needs to be accounted for. The desired outputdataset can be defined as the sum of the enhanced dataset and thesuppressed residual components:

ŝ _(j)(t)=s _(j)(t)+δs _(j)(t).  (4)

In equation (4), ŝ_(j)(t) is the j-th desired output trace and isdefined as the sum of the j-th trace from the enhanced dataset and thej-th suppressed residual component. Because ŝ_(j)(t) includes thesuppressed residual component, ŝ_(j)(t) has a wider frequency band(particularly in the high-frequency region) than s_(j)(t).

To gain further insight on the datasets, the datasets are analyzed inthe frequency domain. In the frequency domain, a seismic trace isdescribed in terms of amplitudes and phases at certain frequencies. Inparticular, a seismic trace is represented using equation (5):

X _(j)(w)=|X _(j)(w)|e ^(iφ(w)).  (5)

In equation (5), the amplitude spectrum |X_(j)(w)| and the phasespectrum φ(w) taken together uniquely describe the time signature of theseismic trace. Additionally, in equation (5), the arrival timeinformation is encoded in the phase spectrum. Therefore, if the phasespectrum remains intact, the seismic trace can be accuratelyreconstructed in terms of the positions where the seismic trace shouldbe located in time (even if the amplitude spectrum is perturbed).

Because the enhanced dataset is constructed using local traveltimeinformation about desired arrivals, it can be assumed that the phasespectra of the enhanced dataset is an adequate estimate of the phasespectra of the desired signals (if the stacking apertures have beenreasonably selected). This assumption can be made because it is known inthe practice of seismic exploration that the arrival time of desiredwaves is contained in the phase spectrum of a seismic trace. Therefore,it is expected that positions/traveltimes of reflected events (forexample, those that are encoded in the phase part of the spectra) andwaveforms are correctly estimated (if the stacking apertures have beenreasonably selected). Stacking apertures are reasonably selected bytaking into account a tradeoff between signal-to-noise ratio improvementand over smoothing of output data after enhancement. Usually, aperturewidths vary in the range of tens to several hundred meters (for example,on the order of 50-500 meters). The use of too large stacking aperturesmay distort the waveform of reflected arrivals.

Although the phase spectra of the enhanced dataset is an adequateestimate of the phase spectra of the desired signals, the enhanceddataset suppresses residual components of the signal (for example,high-frequency components). The suppression is presented in theamplitude spectrum of the enhanced dataset.

In an embodiment, the disclosed seismic processing methods generate anoutput trace by re-combining an amplitude spectrum of an original tracewith the phase spectrum of a corresponding enhanced trace. To accountfor the non-stationary nature of seismic signals (that is, that thestatistical properties of seismic signals vary with time), the seismictraces are decomposed into the TF domain using discrete short-timeFourier Transform (STFT). STFT is a Fourier-related transform used todetermine frequency content of local segments of a signal as it changesover time. Computing the STFT involves dividing a longer time signalinto shorter overlapping intervals of equal length and then separatelycomputing the Fourier transform for each interval. As such, a respectiveFourier spectrum is obtained on each time interval of the signal.Continuous STFT of a time dependent function, x(t), is given by:

STFT<x(t)>≡X(τ,v)=∫_(−∞) ^(∞) x(t)W(t−τ)e ^((−i*2πv*t)) dt.  (6)

In equation (6), W(t) is a real and symmetric window function, v isfrequency, and τ is a “time frame” or time of the center of the timewindow used in the STFT. Using equation (6), an STFT real-valued timedependent function (for example, a seismic trace) is transformed into acomplex-valued matrix with one dimension representing the frequency andthe other dimension representing the time-frame axis. The STFT is alsoinvertible. That is, the original signal can be recovered from thetransform using a procedure called Inverse STFT (ISTFT). To perform theinversion, adjacent sliding time windows overlap with one another by atleast half of their length.

In order to use the original and enhanced datasets to construct theoutput dataset, the original and enhanced datasets are first transformedinto the TF domain. For example, to transform Trace1 (the j-th originaltrace) and Trace2 (the corresponding j-th enhanced trace), STFT isapplied to Trace1 and Trace2. The following complex-valued TF spectraare obtained:

X _(j)(k,l)=STFT<Trace1>,  (7.1)

S _(j)(k,l)=STFT<Trace2>,  (7.2)

N _(j)(k,l)=X _(j)(k,l)−S _(j)(k,l).  (7.3)

In these equations, k is the discrete frequency bin, and l is the frameindices. Equation (7.1) represents the TF spectrum of the j-th originaltrace; equation (7.2) represents the TF spectrum of the correspondingj-th enhanced trace; and equation (7.3) represents the TF spectrum ofthe j-th noise component.

Using equation (5), the TF spectra (7.1) and (7.2) can also berepresented as:

X _(j)(k,l)=|X _(j)(k,l)|e ^(iφ) ^(x) ^((k,l)),  (8)

S _(j)(k,l)=|S _(j)(k,l)|e ^(iφ) ^(s) ^((k,l)).  (9)

In equations (8) and (9), |X_(j)(k,l)| is the amplitude spectrum of thej-th original trace, φ_(X) is the phase spectrum of the j-th originaltrace, |S_(j)(k,l)| is the amplitude spectrum of the corresponding j-thenhanced trace, and cps is the phase spectrum of the corresponding j-thenhanced trace.

a. Method 1

In an embodiment, the first seismic processing method (“Method 1”)constructs a TF spectrum of an output trace by combining the amplitudespectrum of an original trace with the phase spectrum of a correspondingenhanced trace. Using the TF spectra equations (8) and (9), the TFspectrum of the output trace is defined as:

Ŝ _(j)(k,l)=|X _(j)(k,l)|e ^(iφ) ^(s) ^((k,l)).  (10)

As shown by equation (10), the TF spectrum of the j-th output trace,Ŝ_(j)(k,l), is constructed by re-combining the amplitude spectrum of thej-th original trace, |X_(j)(k,l)|, with the phase spectrum of thecorresponding j-th enhanced trace, φ_(s)(k,l). Once the TF spectrum ofthe output trace is generated, ISTFT can be used to obtain thetime-domain output trace:

ŝ _(j)(t)=ISTFT<Ŝ _(j)(k,l)>.  (11)

In equation (11), ŝ_(j)(t) is the time domain output trace.

FIG. 1 is a flow chart of an example method 100 for constructing anoutput trace, according to some implementations. For clarity ofpresentation, the description that follows generally describes method100 in the context of the other figures in this description. Forexample, method 100 can be performed by a computer system described inFIG. 10. However, it will be understood that method 100 may beperformed, for example, by any suitable system, environment, software,and hardware, or a combination of systems, environments, software, andhardware, as appropriate. In some implementations, various steps ofmethod 100 can be run in parallel, in combination, in loops, or in anyorder.

At step 102, method 100 involves generating a first time-frequencyspectrum of a first seismic trace from an original seismic dataset. Theoriginal seismic dataset is a dataset of seismic traces that has beenobtained by performing a seismic survey (for example, seismic surveyillustrated in FIG. 9). In some examples, the original seismic datasethas passed through a standard seismic signal processing workflow thatincludes processes such as noise removal, static correction, anddeconvolution. Therefore, the original seismic dataset is ready forvelocity analysis and imaging. In an example, generating the firsttime-frequency spectrum is performed using short-time Fourier transform(STFT).

At step 104, method 100 generating a second time-frequency spectrum of asecond seismic trace from an enhanced seismic dataset, where the secondseismic trace corresponds to the first seismic trace. In animplementation, the enhanced dataset is generated by applying an SNRenhancement procedure to the original seismic dataset. The enhanceddataset retains the same acquisition geometry as the original dataset.Therefore, the second seismic trace, which corresponds to the firstseismic signal, is located at the same position in the enhanced datasetas the position of the first seismic trace in the original seismicdataset. Furthermore, the enhanced dataset has improved SNR incomparison to the original dataset. However, the high-frequency contentof the enhanced dataset is suppressed due to suboptimal stacking duringthe SNR enhancement procedure.

At step 106, method 100 involves re-combining an amplitude spectrum ofthe first time-frequency spectrum and a phase spectrum of the secondtime-frequency spectrum to generate a third time-frequency spectrum ofan output trace that corresponds to the first and second seismic traces.The amplitude spectrum of the third time-frequency spectrum includeshigher frequencies than the amplitude spectrum of the secondtime-frequency spectrum. Additionally, the frequency band of the outputtrace is wider than the frequency band of the enhanced trace.

In an implementation, once step 106 is completed, method 100 involvesrepeating steps 102-106 for one or more other traces of the originaldataset. The output traces are then arranged together to form an outputdataset. The amplitude spectra of the output dataset includes higherfrequencies than the amplitude spectra of the enhanced dataset.Additionally, the frequency band of the output dataset is wider than thefrequency band of the enhanced dataset. Furthermore, the output datasetpreserves the SNR enhancement found in the enhanced dataset. Thus, theoutput dataset combines the wide frequency band of the original datasetwith the SNR enhancement of the enhanced dataset.

Furthermore, in some implementations, method 100 involves performingISTFT on the TF spectrum of the output trace to generate a time domainversion of the output trace. The ISTFT can be performed on each outputtrace individually once the trace is generated or can be performed onthe output traces once the output dataset is generated.

In Method 1, the frequency content of the signals is preserved. However,the amplitude spectra from the original traces are passed essentiallyuntouched to the output traces. As a result, in the presence of strongnoise, distortion by noise in the amplitude spectra remains uncorrectedin the output traces. Furthermore, the extension of the amplitudespectra of the output traces to a higher-frequency band will be producednot only due to residual original signal components δs_(j)(t), which areabsent in the enhanced dataset, but also due to pure noise {circumflexover (n)}_(j)(t). Despite this, Method 1 has practical value,particularly because cleanup of the phase spectra facilitates generatingvisible (yet contaminated) reflected events. In the absence of thereliable phase spectra derived in Method 1, seismic traces often remainobscured and invisible.

In order to improve an output dataset, the signal components must beimproved. Additionally, the noise components must be suppressed. At theonset of processing the datasets, very little is known about the truedistribution of the amplitude spectrum of the noise. Therefore,improving the output dataset is challenging. In order to improve theoutput dataset, the following assumptions are made at the onset ofprocessing the datasets. First, the available information includes arough signal estimation obtained from a data enhancement procedure.Second, the available information includes a reliable estimation of thephase spectra of the desired output signal. Third, the higher frequencycomponents of the amplitude spectrum of the enhanced dataset may besuppressed. Methods 2 and 3 are based on these assumptions.

b. Method 2

In an embodiment, the second seismic processing method (“Method 2”) usesa Time-Frequency Mask (TFM) for signal and noise separation whengenerating an output dataset. In particular, Method 2 uses the TFM tosuppress the impact of noise presented in the amplitude spectra of theoriginal dataset. Thus, Method 2 at least partially corrects the noisedistortion in the amplitude spectra of the original dataset.

i. Overview of Time-Frequency Masks (TFMs)

TFMs preserve a signal contribution and suppress a noise contribution inthe TF spectrum of a noisy signal. TFMs do so by operating with a simplereal-valued function that is close to 1 in a “signal dominance” regionof the TF spectrum and that is close to 0 in a “noise dominance” region.Applying a TFM to the noisy signal preserves the signal contribution asthe signal contribution is multiplied by 1 and suppresses the noisecontribution as the noise contribution is multiplied by 0.

In the frequency domain, a noisy signal spectrum is defined as a sum ofan actual signal spectrum (that is, the signal contribution) and a noisespectrum (that is, the noise contribution):

X(τ,v)=S(τ,v)+N(τ,v).  (12)

In equation (12), X(τ,v) represents the noisy signal spectrum; S(τ,v)represents the actual signal spectrum; and N(τ,v) represents the noisespectrum. To obtain an estimate of the actual signal spectrum, Ŝ(τ,v),the noisy signal spectrum is multiplied by a real-valued TFM function:

Ŝ(τ,v)=M(τ,v)·X(τ,v).  (13)

In equation (13), M(τ,v) is the real-valued TFM function. This step ofapplying the real-valued TFM to the noisy signal spectrum is referred toas noise suppression.

In practice, at least an approximate behavior of a signal powerspectrum, a noise power spectrum, or both, must be known in order toconstruct a TFM. This is because many TFMs are defined by a relationshipbetween the signal power spectrum, |S(τ,v)|², and the noise powerspectrum, |N(τ,v)|².

There are different types of commercially available TFMs. A first typeof TFM, called Ideal Binary Mask (IBM), is defined as:

$\begin{matrix}{{{IB}{M\left( {\tau,v} \right)}} = \left\{ \begin{matrix}{1,} & {{{if}\mspace{14mu}{{S\left( {\tau,v} \right)}}^{2}} > {{N\left( {\tau,v} \right)}}^{2}} \\{0,} & {else}\end{matrix} \right.} & (14)\end{matrix}$

As shown by equation (14), the value of IBM is 1 where the signal powerspectrum is greater than the noise power spectrum. Otherwise, the valueof IBM is 0. A second type of TFM, called Ideal Rationale Mask (IRM), isdefined as:

$\begin{matrix}{{{IB}{M\left( {\tau,v} \right)}} = {\sqrt{\frac{{{S\left( {\tau,v} \right)}}^{2}}{{{S\left( {\tau,v} \right)}}^{2} + {{N\left( {\tau,v} \right)}}^{2}}}.}} & (15)\end{matrix}$

As shown by equations (14) and (15), IBM and IRM vary in the interval [01]. A third type of TFM is called optimal ratio mask (ORM). This maskachieves optimal SNR gain over all other ratio masks. That is, the ORMprovides the best SNR gain in comparison to the other described TFMs.Theoretical analysis has shown that ORM improves the SNR approximately10 log₁₀ 2 decibels (dB) over IRM, which is considered a simplifiedversion of ORM. ORM is defined as:

$\begin{matrix}{{{OR}{M\left( {\tau,v} \right)}} = {{\frac{1}{2}\left\lbrack {1 + \frac{{{S\left( {\tau,v} \right)}}^{2} - {{N\left( {\tau,v} \right)}}^{2}}{{{X\left( {\tau,v} \right)}}^{2}}} \right\rbrack}.}} & (16)\end{matrix}$

By definition, |X(τ,v)|²=|S(τ,v)+N(τ,v)|². Furthermore, as shown byequations (14), (15), and (16), IBM, IRM, and ORM are power spectrumdependent only. That is, IBM, IRM, and ORM do not consider phaseinformation of the noisy signal.

Some types of TFMs consider phase information of the noisy signal. Afourth type of TFM, called phase-sensitive mask (PSM), considers phaseinformation of the noisy signal. PSM uses phase information to correctan amplitude spectrum of the noisy signal while leaving the phasespectrum untouched. PSM is defined as:

$\begin{matrix}{{{PSM}\left( {\tau,v} \right)} = {\frac{{S\left( {\tau,v} \right)}}{{X\left( {\tau,v} \right)}}{{\cos\left( {\varphi_{S} - \varphi_{X}} \right)}.}}} & (17)\end{matrix}$

In equation (17), φ_(s) is the phase spectrum of the signal S(τ,v), andφ_(x) is the phase spectrum of the noisy signal X(τ,v). Furthermore, asshown by equation (17), PSM varies in the interval [−1, 1].

ii. Description of Method 2

Given that TFMs can preserve a signal contribution and suppress a noisecontribution in a noisy signal, it would be useful to apply TFMs whenconstructing an output trace in order to suppress the noise contributionin the original trace. As explained previously, at least an approximatebehavior of a signal power spectrum, a noise power spectrum, or both,must be known in order to construct a TFM. However, unlike other typesof signals, signal or noise estimates are not available in seismicprospecting. Therefore, TFMs, such as those previously described, cannotbe directly used in seismic data processing.

In an embodiment, to counteract the unavailability of signal or noiseestimates, Method 2 uses an enhanced trace to derive signal and noiseestimates to construct TFMs. In particular, the enhanced trace is usedas a “proxy,” or estimate, of the desired output trace. And thedifference between the original trace and the enhanced trace is used asan estimate of the noise contribution in the original trace. Theenhanced trace and the noise estimate can then be used to constructTFMs. Specifically, the enhanced trace and the noise estimate are usedto respectively calculate the signal power spectrum, |S(τ,v)|², and thenoise power spectrum, |N(τ,v)|². The enhanced traces are used to replaceS(τ,v) and the noise estimate is calculated as: N(τ,v)=X(k,l)−S(k,l).

However, because the enhanced trace and the noise contribution areapproximations, part of the actual signal may leak into the noiseestimate. Therefore, as shown by equation (3), the noise estimate mayinclude an actual noise component and a residual signal component. It ischallenging to separate and characterize the residual signal componentthat leaks into the noise estimate.

In an embodiment, TFMs are modified to account for the residual signalcomponent that leaks into the noise estimate. In an implementation, TFMsare modified to include a noise threshold value, ε, that is designed tocontrol the permissible power of noise in TFMs. In particular, the valueof the noise threshold, which by definition is less than one (that is,ε<1), can increase or decrease the permissible power of noise. Byintroducing the noise threshold, even if the actual noise component andresidual signal component in the noise estimate are not completelyseparated, some noise can be accepted in the noise estimate in exchangefor preserving at least a portion of the residual signal component.

In an example, IRM is modified to include the noise threshold. Themodified IRM (MIRM) is defined as:

$\begin{matrix}{{{{MIRM}\left( {\tau,v} \right)} = \sqrt{\frac{{{S\left( {\tau,v} \right)}}^{2}}{{{S\left( {\tau,v} \right)}}^{2} + {ɛ{{N\left( {\tau,v} \right)}}^{2}}}}},{ɛ < {1.}}} & (18)\end{matrix}$

In another example, ORM is modified to include the noise threshold. Themodified MORM (MORM) is defined as:

$\begin{matrix}{{{{MORM}\left( {\tau,v} \right)} = {\frac{1}{2}\left\lbrack {1 + \frac{{{S\left( {\tau,v} \right)}}^{2} - {ɛ{{N\left( {\tau,v} \right)}}^{2}}}{{{X\left( {\tau,v} \right)}}^{2}}} \right\rbrack}},{ɛ < {1.}}} & (19)\end{matrix}$

As shown in equations (18) and (19), the value of the noise threshold Evaries between 0 and 1 and controls a degree of “noise passing.” Withintermediate values of E between 0 and 1, some amount of noise ispassed. Specifically, smaller noise threshold values pass less noise,and greater noise threshold values pass more noise. In animplementation, the threshold value is defined by taking into accountthe tradeoff between high-frequency band preservation andsignal-to-noise ratio improvement. That is, the fact that higherfrequency band extension may be mainly obtained due to noise must betaken into consideration. Therefore, the value of the noise threshold is“case-specific” and can be established experimentally. In an example,the noise threshold has a default value of 0.5. In some implementations,the noise threshold is time-frame and frequency dependent. In suchimplementations, the expression for the threshold value is ε(τ,v).Time-frequency masking is a local and point-dependent procedure. Assuch, in principle, ε(τ,v) may be determined in each point of thetime-frequency spectrum.

In another implementation, phase-sensitive TFMs are also modified. In afirst example, PSM is combined with MIRM to form a phase-sensitive IRMthat is defined as:

PSMIRM(τ,v)=MIRM(τ,v)·cos(φ_(s)−φ_(x))  (20)

In a second example, PSM is combined with MORM to form a phase-sensitiveORM that is defined as:

PSMORM(τ,v)=MORM(τ,v)·cos(φ_(s)−φ_(x)).  (21)

In equations (20) and (21), φ_(X), φ_(S) are the phase spectra of theoriginal and enhanced traces, respectively.

These modified TFMs can be used to generate an output trace with visiblearrivals of reflected waves so that the amplitude spectrum of the traceis sufficiently expanded to higher frequencies. When using TFMs, thetime-frequency masking is performed in a trace-by-trace manner (that is,single-channel processing).

In a first embodiment, a modified power spectrum dependent TFM (forexample, MIRM or MORM) is applied to a noisy signal spectrum to suppressthe noise component of the noisy signal spectrum, thereby generating anoutput dataset spectrum Ŝ(τ,v). In particular, as shown in equation(15), the output spectrum is obtained by multiplying the noisy signalspectrum by a TFM function. Here, the noisy signal spectrum is thesignal spectrum that is constructed from the original trace spectrum andthe enhanced trace spectrum. Accordingly, the TF spectrum of the outputdataset is represented by one of the following equations (depending onthe choice of mask):

Ŝ _(j)(k,l)=|X _(j)(k,l)|e ^(iφ) ^(s) ^((k,l))·MIRM(k,l).  (22)

Ŝ _(j)(k,l)=|X _(j)(k,l)|e ^(iφ) ^(s) ^((k,l))·MORM(k,l).  (23)

In equations (22) and (23), Ŝ_(j)(k,l) is the TF spectrum of the j-thoutput trace, |X_(j)(k,l)| is the TF amplitude spectrum of the j-thoriginal trace, and φ_(s)(k,l) is the TF phase spectrum of thecorresponding j-th enhanced trace. Equation (22) uses MIRM as the TFMand equation (23) uses MORM as the TFM.

In a second embodiment, a phase-sensitive TFM is applied to a noisysignal spectrum to generate an output spectrum Ŝ(τ,v). Unlike power oramplitude spectrum dependent TFMs, phase-sensitive TFMs are directlyapplied to the full complex TF spectrum of the original trace.Therefore, there is no direct enhanced phase spectrum implantation.Rather, the phase corrections are performed in the original phasespectrum by the phase-sensitive TFMs. Accordingly, the TF desired outputspectra that are derived using the phase-sensitive TFMs are representedby one of the following equations (depending on the choice of mask):

Ŝ _(j)(k,l)=X _(j)(k,l)·PSMIRM(k,l).  (24)

Ŝ _(j)(k,l)=X _(j)(k,l)·PSMORM(k,l).  (25)

In equations (24) and (25), X_(j)(k,l) is the full complex TF spectrumof original trace. Equation (24) uses PSMIRM as the TFM and equation(25) uses PSMORM as the TFM.

FIG. 2 is a flow chart of an example method 200 for constructing adesired output trace, according to some implementations. For clarity ofpresentation, the description that follows generally describes method200 in the context of the other figures in this description. Forexample, method 200 can be performed by a computer system described inFIG. 10. However, it will be understood that method 200 may beperformed, for example, by any suitable system, environment, software,and hardware, or a combination of systems, environments, software, andhardware, as appropriate. In some implementations, various steps ofmethod 200 can be run in parallel, in combination, in loops, or in anyorder.

At step 202, method 200 involves generating a first time-frequencyspectrum of a first seismic trace from an original seismic dataset. Theoriginal seismic dataset is a dataset of seismic traces that has beenobtained by performing a seismic survey (for example, seismic surveyillustrated in FIG. 9). In some examples, the original seismic datasethas passed through a standard seismic signal processing workflow thatincludes processes such as noise removal, static correction, anddeconvolution. Therefore, the original seismic dataset is ready forvelocity analysis and imaging. Performing the time-frequencytransformation on the first seismic trace from the original seismicdataset generates a time-frequency spectrum of the first seismic trace.In an example, the time-frequency transformation is performed usingshort-time Fourier transform (STFT).

At step 204, method 200 involves generating a second time-frequencyspectrum of a second seismic trace from an enhanced seismic dataset,wherein the second seismic trace corresponds to the first seismic trace.In an implementation, the enhanced dataset is generated by applying anSNR enhancement procedure to the original seismic dataset. The enhanceddataset retains the same acquisition geometry as the original dataset.Therefore, the second seismic trace, which corresponds to the firstseismic signal, is located at the same position in the enhanced datasetas the position of the first seismic trace in the original seismicdataset. Furthermore, the enhanced dataset has improved SNR incomparison to the original dataset. However, the high-frequency contentof the enhanced dataset is suppressed due to suboptimal stacking duringthe SNR enhancement procedure.

At step 206, method 200 involves calculating a difference between thefirst time-frequency spectrum and the second time-frequency spectrum togenerate a noise estimate in the first seismic trace. This calculationis represented by equation (26):

N _(j)(k,l)=X _(j)(k,l)−S _(j)(k,l).  (26)

The noise estimate includes an actual noise component and a suppressedresidual component of the signal.

At step 208, method 200 involves constructing, based on (i) the noiseestimate, (ii) the first time-frequency spectrum, and (iii) the secondtime-frequency spectrum, a time-frequency mask (TFM). In oneimplementation, the constructed TFM is a power spectrum dependent TFM,such as MIRM and MORM. In another implementation, the constructed TFM isa phase-sensitive TFM, such as PSMIRM and PSMORM.

At step 210, method 200 involves using the constructed TFM to generate athird time-frequency spectrum of an output trace that corresponds to thefirst and second seismic traces. In a first example, the constructed TFMis a MIRM. In this example, using the constructed TFM to generate theoutput seismic trace involves determining the value of MIRM. Determiningthe value of MIRM involves determining whether the absolute value of theamplitude spectrum of the original signal is equal to zero(|X_(j)(k,l)|=0). If the absolute value of the amplitude spectrum isequal to zero, then MIRM is set equal to one. Otherwise, if the absolutevalue of the amplitude spectrum of the original signal is not equal tozero (|X_(j)(k,l)|≠0), then MIRM is calculated according to equation(18). Once the value of MIRM is determined, the output trace isgenerated according to equation (22). For simplicity, the version ofMethod 2 that uses MIRM as the TFM is referred to as Method 2.1.

In a second example, the constructed TFM is a MORM. In this example,using the constructed TFM to generate the output seismic trace involvesdetermining the value of MORM. Determining the value of MORM involveswhether the absolute value of the amplitude spectrum of the originalsignal is equal to zero (|X_(j)(k,l)|=0). If the absolute value of theamplitude spectrum is equal to zero, then MORM is set equal to one.Otherwise, if the absolute value of the amplitude spectrum of theoriginal signal is not equal to zero (|X_(j)(k,l)|≠0), then it isdetermined whether the absolute value of the amplitude spectrum of thenoise estimate is less than or equal to the absolute value of theamplitude spectrum (|N_(j)(k,l)|≤|X_(j)(k,l)|). If the absolute value ofthe amplitude spectrum of the noise estimate is less than or equal tothe absolute value of the amplitude spectrum, then the value of MORM iscalculated according to equation (19). Otherwise, if the absolute valueof the amplitude spectrum of the noise estimate is not less than orequal to the absolute value of the amplitude spectrum, then the value ofMORM is equal to the ratio of the amplitude spectrum of the enhancedtrace to the amplitude spectrum of the original trace:

$\begin{matrix}{{{MORM}\left( {k,l} \right)} = {\frac{{S_{j}\left( {k,l} \right)}}{{X_{j}\left( {k,l} \right)}}.}} & (27)\end{matrix}$

Once the value of MORM is determined, the output trace is generatedaccording to equation (23). For simplicity, the version of Method 2 thatuses MORM as the TFM is referred to as Method 2.2.

In a third example, the constructed TFM is a PSMIRM. In this example,using the constructed TFM to generate the output seismic trace involvesdetermining the value of PSMIRM. Determining the value of PSMIRMinvolves determining whether the absolute value of the amplitudespectrum of the original signal is equal to zero (|X_(j)(k,l)|=0). Ifthe absolute value of the amplitude spectrum is equal to zero, thenPSMIRM is set equal to one. Otherwise, if the absolute value of theamplitude spectrum of the original signal is not equal to zero(|X_(j)(k,l)|≠0), then the value of PSMIRM is calculated according toequation (20). Once the value of PSMIRM is determined, the output traceis generated according to equation (24). For simplicity, the version ofMethod 2 that uses PSMIRM as the TFM is referred to as Method 2.3.

In a fourth example, the constructed TFM is a PSMORM. In this example,using the constructed TFM to generate the output seismic trace involvesdetermining the value of PSMORM. Determining the value of PSMORMinvolves whether the absolute value of the amplitude spectrum of theoriginal signal is equal to zero (|X_(j)(k,l)|=0). If the absolute valueof the amplitude spectrum is equal to zero, then PSMORM is set equal toone. Otherwise, if the absolute value of the amplitude spectrum of theoriginal signal is not equal to zero (|X_(j)(k,l)|≠0), then it isdetermined whether the absolute value of the amplitude spectrum of thenoise estimate is less than or equal to the absolute value of theamplitude spectrum (|N_(j)(k,l)|≤|X_(j)(k,l)|). If the absolute value ofthe amplitude spectrum of the noise estimate is less than or equal tothe absolute value of the amplitude spectrum, then the value of PSMORMis calculated according to equation (21). Otherwise, if the absolutevalue of the amplitude spectrum of the noise estimate is not less thanor equal to the absolute value of the amplitude spectrum, then the valueof PSMORM is equal to the ratio of the amplitude spectrum of theenhanced trace to the amplitude spectrum of the original trace. Once thevalue of MORM is determined, the output trace is generated according toequation (25). For simplicity, the version of Method 2 that uses MORM asthe TFM is referred to as Method 2.4.

In an implementation, once step 210 is completed, method 200 involvesrepeating steps 202-210 for one or more other traces in the originalseismic dataset. The output traces are then arranged together to form anoutput dataset. The amplitude spectra of the output dataset includeshigher frequencies than the amplitude spectra of the enhanced dataset.Additionally, the frequency band of the output dataset is wider than thefrequency band of the enhanced dataset. Furthermore, the output datasetpreserves the SNR enhancement found in the enhanced dataset. Thus, theoutput dataset combines the wide frequency band of the original datasetwith the SNR enhancement of the enhanced dataset. Additionally,application of TFMs reduces identified noises that remain untouched inMethod 1.

Furthermore, in some implementations, method 200 also involvesperforming ISTFT on the TF spectrum of the output trace to generate atime domain version of the output trace. The ISTFT can be performed oneach output trace individually once the trace is generated or can beperformed on the output traces once the output dataset is generated.

c. Method 3

As explained previously, the noise component of an original trace isdefined as the difference between the original trace and a correspondingenhanced trace. As also explained, this noise estimate includes both anactual noise component and a residual component of the actual signalthat has been suppressed due to suboptimal stacking. In an embodiment,the third method (“Method 3”) involves estimating the actual noisecomponent in the original traces. The estimate of the actual noisecomponent is used to generate a TFM that is then used to construct anoutput trace.

In an embodiment, the noise component, n_(j)(t), is characterized asWhite Gaussian Noise (WGN). In this embodiment, the level of WGN isnearly identical within each time interval of a trace underconsideration. By characterizing the noise component as WGN, thehigh-amplitude outliers in n_(j)(t) that are due to imperfectsubtraction of coherent arrivals representing parts of the leaked signalcan be removed. To do so, it is presumed that the level of WGN is lessthan peak amplitudes of desired arrivals. In an implementation, thehigh-amplitude outliers are removed by taking the median of thedifference between noisy and enhanced traces (instead of using the fulldistribution of noise). In an example, a median filter is used to takethe median difference between the noisy and enhanced traces.

Method 3 includes two stages: a noise estimation stage and a TF maskingstage. The second stage is performed in analogy with Method 2, with onemodification: the TF spectra of noise {circumflex over (N)}_(j)(k,l) iscalculated as discrete STFT (DSTFT) of “noise” estimated during thenoise estimation stage (as opposed to the difference of TF spectra of anoriginal trace and an enhanced trace as was done in Method 2).

In the noise estimation stage, the noise component is calculated asn_(j)(t)=x_(j)(t)−s_(j)(t). Then, the TF spectrum of the noisecomponent, N_(j)(k,l), is generated using STFT. Once N_(j)(k,l) isgenerated, a respective median value of the respective amplitudespectrum at each frequency in the noise spectrum is calculated:

$\begin{matrix}{{M(k)} = {\underset{l}{median}\mspace{14mu}{{{N_{j}\left( {k,l} \right)}}.}}} & (28)\end{matrix}$

In equation (28), k is the frequency and j is the trace number. Once therespective median value at each frequency is calculated, a TF spectrumof a refined noise estimate is calculated as:

{circumflex over (N)} _(j)(k,l)=M(k)·e ^(iφ) ^(N) ^((k,l)).  (29)

In equation (29), {circumflex over (N)}_(j)(k,l) is the TF spectrum ofthe refined noise estimate and φ_(N) is the phase spectrum of theinitial noise estimate. In this example, the noise component ischaracterized as WGN. However, other methods for single-channel noiseestimation are possible and contemplated.

In the TF masking stage, the refined noise estimate is used to generatea TFM. In an implementation, methods 2.1, 2.2, 2.3, and 2.4 are modifiedto introduce the refined noise estimate so that the TFMs are generatedusing the refined noise estimate. In particular, the refined noiseestimate, {circumflex over (n)}_(j)(t), replaces the initial noiseestimate, n_(j)(t). The modified methods are referred to as methods 3.1,3.2, 3.3, and 3.4, respectively.

FIG. 3 is a flow chart of an example method 300 for constructing adesired output trace, according to some implementations. For clarity ofpresentation, the description that follows generally describes method300 in the context of the other figures in this description. Forexample, method 300 can be performed by a computer system described inFIG. 10. However, it will be understood that method 300 may beperformed, for example, by any suitable system, environment, software,and hardware, or a combination of systems, environments, software, andhardware, as appropriate. In some implementations, various steps ofmethod 300 can be run in parallel, in combination, in loops, or in anyorder.

At step 302, method 300 involves generating a first time-frequencyspectrum of a first seismic trace from an original seismic dataset. Theoriginal seismic dataset is a dataset of seismic traces that has beenobtained by performing a seismic survey (for example, seismic surveyillustrated in FIG. 9). In some examples, the original seismic datasethas passed through a standard seismic signal processing workflow thatincludes processes such as noise removal, static correction, anddeconvolution. Therefore, the original seismic dataset is ready forvelocity analysis and imaging. Performing the time-frequencytransformation on the first seismic trace from the original seismicdataset generates a time-frequency spectrum of the first seismic trace.In an example, the time-frequency transformation is performed usingshort-time Fourier transform (STFT).

At step 304, method 300 involves generating a second time-frequencyspectrum of a second seismic trace from an enhanced seismic dataset,where the second seismic trace corresponds to the first seismic trace.In an implementation, the enhanced dataset is generated by applying anSNR enhancement procedure to the original seismic dataset. The enhanceddataset retains the same acquisition geometry as the original dataset.Therefore, the second seismic trace, which corresponds to the firstseismic signal, is located at the same position in the enhanced datasetas the position of the first seismic trace in the original seismicdataset. Furthermore, the enhanced dataset has improved SNR incomparison to the original dataset. However, the high-frequency contentof the enhanced dataset is suppressed due to suboptimal stacking duringthe SNR enhancement procedure.

At step 306, method 300 involves calculating a difference between thefirst time-frequency spectrum and the second time-frequency spectrum togenerate a noise estimate of noise in the first seismic trace.

At step 308, method 300 involves characterizing the initial noiseestimate as White Gaussian Noise (WGN).

At step 310, method 300 involves calculating, based on thecharacterization of the initial noise estimate, a third time-frequencyspectrum of a refined noise estimate. Calculating, based on thecharacterization of the initial noise estimate, a refined noise estimateincludes: for each frequency in the initial noise estimate, calculatinga respective median of an amplitude spectrum of the initial noiseestimate at that frequency. Additionally, the calculating includescoupling each respective median of the amplitude spectrum and acorresponding respective phase spectrum of the initial noise to generatethe time-frequency spectrum of the refined noise estimate.

At step 312, method 300 involves constructing, based on the firsttime-frequency spectrum, the second time-frequency spectrum, and thethird time-frequency spectrum, a time-frequency mask (TFM).

At step 314, method 300 involves using the constructed TFM to generate afourth time-frequency spectrum of an output trace that corresponds tothe first and second seismic traces.

II. Real Data Examples

FIGS. 4A-4D illustrate an example of the disclosed two-step processapplied to a seismic trace, according to some implementations. In thisexample, the two-step process is applied to the seismic dataset in orderto improve the SNR of the seismic dataset while preservinghigh-frequency content of the dataset. In the first step, non-linearbeamforming (NLBF) is used to obtain an enhanced trace from the originaltrace. In the second step, Method 2 is used to generate the outputtrace.

FIG. 4A illustrates a time-frequency spectrum 400 of an original seismictrace. The time-frequency spectrum 400 is generated by using STFT totransform the original trace from the time domain to the time-frequencyspectrum domain. As shown in FIG. 4A, the time-frequency spectrum 400 isa three-dimensional (3D) representation of the original trace. As shownin FIG. 4A, the frequency information in the original trace is weak andthere is little decipherable information.

FIG. 4B illustrates a time-frequency spectrum 410 of an enhanced seismictrace that is generated by applying an SNR enhancement procedure to theoriginal trace. In particular, a non-linear beamforming (NLBF) processis applied to the original trace in order to generate the enhancedtrace. As described previously, the SNR enhancement procedure improvesthe signal-to-noise ratio of the original trace. However, as shown inFIG. 4B, although the quality of the signal improves in lowerfrequencies, the high-frequency content of the signal is suppressed. Forexample, amplitudes at frequencies in the range of 5-10 Hertz (Hz)experience significant uplift and enhancement. However, as also shown bycomparing FIGS. 4A and 4B, that signal is suppressed in the frequencyrange 15-20 Hz.

FIG. 4C illustrates a time-frequency spectrum 420 of an estimate of thenoise in the original trace. In this example, the noise estimate isgenerated by calculating the difference between the original trace andthe enhanced trace.

FIG. 4D illustrates a time-frequency spectrum 430 of an output tracethat is generated using the original trace, the enhanced trace, and thenoise estimate. In this example, the output seismic trace used Method2.3. That is, PSMIRM is used as the TFM in this application of Method 2.As shown by comparing FIG. 4D to FIGS. 4A-4B, the output trace hasimproved SNR compared to the original trace while preserving thehigh-frequency content.

FIGS. 5A-5C illustrate an example application of the disclosed two-stepprocess to a seismic dataset. In this example, non-linear beamforming(NLBF) is used in the first stage, and Method 1 is used in the secondstage.

FIG. 5A illustrates an original dataset 500 in the time domain. In thisexample, the original dataset 500 is a common-midpoint (CMP) gather thatis obtained from a three-dimensional (3D) land dataset. Additionally,the original dataset 500 has passed through a standard processingworkflow. Therefore, the original dataset 500 is ready for velocityanalysis and imaging. As shown in FIG. 5A, the prestack signal is weakand there are no visible reflections in the gather.

FIG. 5B illustrates an enhanced dataset 510 that is generated byapplying an SNR enhancement procedure to the original dataset 500. Inthis example, a non-linear beamforming (NLBF) method is applied to theoriginal dataset 500 to generate the enhanced seismic dataset 510.Furthermore, in this example, the NLBF data enhancement is performedwith summation apertures 150 meters×150 meters in the CMP and offsetdimensions. Approximately 200 neighboring traces are used in the localsummation to enhance each trace in the original dataset. As shown inFIG. 5B, after the applying the enhancement procedure, the reflectionsare recognizable in the entire offset range. However, the high-frequencycontent of the gather is suppressed due to suboptimal stacking. This isshown in FIG. 5B by the strong, but overly smoothed, reflections.

FIG. 5C illustrates a first output dataset 520 that is generated usingthe original dataset 500 and the enhanced dataset 510 as buildingblocks. In this example, Method 1 is used to generate the output dataset520.

FIG. 5D illustrates a second output dataset 530 that is also generatedusing the original dataset 500 and the enhanced dataset 510 as buildingblocks. In this example, Method 3.3 is used to generate the secondoutput dataset 530. As described previously, PSMIRM is used as the TFMin Method 3.3.

FIG. 5E illustrates a third output dataset 540 that is also generatedusing the original dataset 500 and the enhanced dataset 510 as buildingblocks. In this example, Method 3.2 is used to generate the outputdataset 540. As described previously, MORM is used as the TFM in Method3.2.

As shown in FIGS. 5C, 5D, and 5E, the reflections, which are stillvisible in the entire offset range, remain resolved with more details incomparison to the enhanced dataset 510. As also shown in these figures,sharp time shifts between neighboring traces are clearly distinguishablemost likely preserving static corrections due to variable near surfaceconditions (unlike FIG. 5B where events are overly smoothed and suchstatic corrections cannot be recovered any more).

FIGS. 6A and 6B each illustrate a comparison of averaged amplitudespectra of an original dataset, an enhanced dataset, and outputdatasets, according to some implementations. Specifically, the averagedamplitude spectra are calculated in the time window [0.5, 3.5] seconds.In this example, the averaged amplitude spectra are constructed using astacked trace (for example, a stack of 10 nearby traces in offsetdirection). Stacked traces are used to stabilize the results: variationson a single trace would be larger, whereas on stacked trace, variationswould be smaller and desired trends in amplitude behavior are moreeasily identified.

FIGS. 6A and 6B each illustrate an original data spectrum 602, anenhanced data spectrum 604, and an output data spectrum 606 that isgenerated using Method 1. FIG. 6A also illustrates an output dataspectrum 608 that is generated using Method 3.3, and FIG. 6B alsoillustrates an output data spectrum 610 that is generated using Method3.2. The computed amplitude spectra validate that introduced correctionsusing the disclosed methods led to preservation of higher frequencies inthe data. In these examples, a 200 millisecond (ms) time window is usedfor STFT and the noise threshold E is chosen as E=0.5.

FIGS. 7A-7C illustrate fragments of stack/time image sections generatedusing original, enhanced, and output data, according to someimplementations. In particular, FIG. 7A illustrates a stack 700 oforiginal data, FIG. 7B illustrates a stack 710 of enhanced data (afterNLBF), and FIG. 7C illustrates a stack 720 of output data that isgenerated using Method 3.3. The prestack data of the stack 720 is shownin FIG. 5D. Comparison of the stacks illustrates that while the enhancedstack 710 has better event continuity in the challenging data area(located between lines 702 a, 702 b), the stacks 710 and 720 possessfiner spatial and temporal details.

FIG. 8 illustrates a comparison of averaged amplitude spectra of anoriginal stack, an enhanced stack, and an output stack, according tosome implementations. Specifically, the averaged amplitude spectra arecalculated in the time window [0.5, 3.5] seconds in zero-offset stacksections. FIG. 8 illustrates an original stack spectrum 802, an enhancedstack spectrum 804, and an output stack spectrum 806 that is generatedusing Method 3.3. As shown by the output stack spectrum 806, higherfrequencies appear after stacking than in prestack data (shown in FIGS.6A and 6B). This indicates that additional signal is gained on prestackrecords that coherently added up during the imaging step. Therefore, itcan be concluded that amplitude spectra corrections provide significantuplift in prestack and post-stack images obtained with challengingseismic data.

IV. Example Seismic Survey

FIG. 9 is a schematic view of a seismic survey being performed to mapsubterranean features such as facies and faults in a subterraneanformation 900. The subterranean formation 900 includes a layer ofimpermeable cap rocks 902 at the surface. Facies underlying theimpermeable cap rocks 902 include a sandstone layer 904, a limestonelayer 906, and a sand layer 908. A fault line 910 extends across thesandstone layer 904 and the limestone layer 906.

A seismic source 912 (for example, a seismic vibrator or an explosion)generates seismic waves 914 that propagate in the earth. The velocity ofthese seismic waves depends on properties such as, for example, density,porosity, and fluid content of the medium through which the seismicwaves are traveling. Different geologic bodies or layers in the earthare distinguishable because the layers have different properties and,thus, different characteristic seismic velocities. For example, in thesubterranean formation 900, the velocity of seismic waves travelingthrough the subterranean formation 900 will be different in thesandstone layer 904, the limestone layer 906, and the sand layer 908. Asthe seismic waves 914 contact interfaces between geologic bodies orlayers that have different velocities, the interface reflects some ofthe energy of the seismic wave and refracts part of the energy of theseismic wave. Such interfaces are sometimes referred to as horizons.

The seismic waves 914 are received by a sensor or sensors 916. Althoughillustrated as a single component in FIG. 1, the sensor or sensors 916are typically a line or an array of sensors 916 that generate an outputsignal in response to received seismic waves including waves reflectedby the horizons in the subterranean formation 900. The sensor or sensors916 can be geophone-receivers that produce electrical output signalstransmitted as input data, for example, to a computer 918 on a seismiccontrol truck 920. Based on the input data, the computer 918 maygenerate a seismic data output such as, for example, a seismic two-wayresponse time plot.

A control center 922 can be operatively coupled to the seismic controltruck 920 and other data acquisition and wellsite systems. The controlcenter 922 may have computer facilities for receiving, storing,processing, and analyzing data from the seismic control truck 920 andother data acquisition and wellsite systems. For example, computersystems 924 in the control center 922 can be configured to analyze,model, control, optimize, or perform management tasks of fieldoperations associated with development and production of resources suchas oil and gas from the subterranean formation 900. Alternatively, thecomputer systems 924 can be located in a different location than thecontrol center 922. Some computer systems are provided withfunctionality for manipulating and analyzing the data, such asperforming seismic interpretation or borehole resistivity image loginterpretation to identify geological surfaces in the subterraneanformation or performing simulation, planning, and optimization ofproduction operations of the wellsite systems.

In some embodiments, results generated by the computer system 924 may bedisplayed for user viewing using local or remote monitors or otherdisplay units. One approach to analyzing seismic data is to associatethe data with portions of a seismic cube representing the subterraneanformation 900. The seismic cube can also display results of the analysisof the seismic data associated with the seismic survey.

V. Example Computer System

FIG. 10 is a block diagram of an example computer system 1000 used toprovide computational functionalities associated with describedalgorithms, methods, functions, processes, flows, and proceduresdescribed in the present disclosure, according to some implementationsof the present disclosure. The illustrated computer 1002 is intended toencompass any computing device such as a server, a desktop computer, alaptop/notebook computer, a wireless data port, a smart phone, apersonal data assistant (PDA), a tablet computing device, or one or moreprocessors within these devices, including physical instances, virtualinstances, or both. The computer 1002 can include input devices such askeypads, keyboards, and touch screens that can accept user information.Also, the computer 1002 can include output devices that can conveyinformation associated with the operation of the computer 1002. Theinformation can include digital data, visual data, audio information, ora combination of information. The information can be presented in agraphical user interface (UI) (or GUI).

The computer 1002 can serve in a role as a client, a network component,a server, a database, a persistency, or components of a computer systemfor performing the subject matter described in the present disclosure.The illustrated computer 1002 is communicably coupled with a network1030. In some implementations, one or more components of the computer1002 can be configured to operate within different environments,including cloud-computing-based environments, local environments, globalenvironments, and combinations of environments.

At a high level, the computer 1002 is an electronic computing deviceoperable to receive, transmit, process, store, and manage data andinformation associated with the described subject matter. According tosome implementations, the computer 1002 can also include, or becommunicably coupled with, an application server, an email server, a webserver, a caching server, a streaming data server, or a combination ofservers.

The computer 1002 can receive requests over network 1030 from a clientapplication (for example, executing on another computer 1002). Thecomputer 1002 can respond to the received requests by processing thereceived requests using software applications. Requests can also be sentto the computer 1002 from internal users (for example, from a commandconsole), external (or third) parties, automated applications, entities,individuals, systems, and computers.

Each of the components of the computer 1002 can communicate using asystem bus 1003. In some implementations, any or all of the componentsof the computer 1002, including hardware or software components, caninterface with each other or the interface 1004 (or a combination ofboth), over the system bus 1003. Interfaces can use an applicationprogramming interface (API) 1012, a service layer 1013, or a combinationof the API 1012 and service layer 1013. The API 1012 can includespecifications for routines, data structures, and object classes. TheAPI 1012 can be either computer-language independent or dependent. TheAPI 1012 can refer to a complete interface, a single function, or a setof APIs.

The service layer 1013 can provide software services to the computer1002 and other components (whether illustrated or not) that arecommunicably coupled to the computer 1002. The functionality of thecomputer 1002 can be accessible for all service consumers using thisservice layer. Software services, such as those provided by the servicelayer 1013, can provide reusable, defined functionalities through adefined interface. For example, the interface can be software written inJAVA, C++, or a language providing data in extensible markup language(XML) format. While illustrated as an integrated component of thecomputer 1002, in alternative implementations, the API 1012 or theservice layer 1013 can be stand-alone components in relation to othercomponents of the computer 1002 and other components communicablycoupled to the computer 1002. Moreover, any or all parts of the API 1012or the service layer 1013 can be implemented as child or sub-modules ofanother software module, enterprise application, or hardware modulewithout departing from the scope of the present disclosure.

The computer 1002 includes an interface 1004. Although illustrated as asingle interface 1004 in FIG. 10, two or more interfaces 1004 can beused according to particular needs, desires, or particularimplementations of the computer 1002 and the described functionality.The interface 1004 can be used by the computer 1002 for communicatingwith other systems that are connected to the network 1030 (whetherillustrated or not) in a distributed environment. Generally, theinterface 1004 can include, or be implemented using, logic encoded insoftware or hardware (or a combination of software and hardware)operable to communicate with the network 1030. More specifically, theinterface 1004 can include software supporting one or more communicationprotocols associated with communications. As such, the network 1030, orthe interface's hardware, can be operable to communicate physicalsignals within and outside of the illustrated computer 1002.

The computer 1002 includes a processor 1005. Although illustrated as asingle processor 1005 in FIG. 10, two or more processors 1005 can beused according to particular needs, desires, or particularimplementations of the computer 1002 and the described functionality.Generally, the processor 1005 can execute instructions and canmanipulate data to perform the operations of the computer 1002,including operations using algorithms, methods, functions, processes,flows, and procedures as described in the present disclosure.

The computer 1002 also includes a database 1006 that can hold data forthe computer 1002 and other components connected to the network 1030(whether illustrated or not). For example, database 1006 can be anin-memory, conventional, or a database storing data consistent with thepresent disclosure. In some implementations, database 1006 can be acombination of two or more different database types (for example, hybridin-memory and conventional databases) according to particular needs,desires, or particular implementations of the computer 1002 and thedescribed functionality. Although illustrated as a single database 1006in FIG. 10, two or more databases (of the same, different, orcombination of types) can be used according to particular needs,desires, or particular implementations of the computer 1002 and thedescribed functionality. While database 1006 is illustrated as aninternal component of the computer 1002, in alternative implementations,database 1006 can be external to the computer

The computer 1002 also includes a memory 1007 that can hold data for thecomputer 1002 or a combination of components connected to the network1030 (whether illustrated or not). Memory 1007 can store any dataconsistent with the present disclosure. In some implementations, memory1007 can be a combination of two or more different types of memory (forexample, a combination of semiconductor and magnetic storage) accordingto particular needs, desires, or particular implementations of thecomputer 1002 and the described functionality. Although illustrated as asingle memory 1007 in FIG. 10, two or more memories 1007 (of the same,different, or combination of types) can be used according to particularneeds, desires, or particular implementations of the computer 1002 andthe described functionality. While memory 1007 is illustrated as aninternal component of the computer 1002, in alternative implementations,memory 1007 can be external to the computer 1002.

The application 1008 can be an algorithmic software engine providingfunctionality according to particular needs, desires, or particularimplementations of the computer 1002 and the described functionality.For example, application 1008 can serve as one or more components,modules, or applications. Further, although illustrated as a singleapplication 1008, the application 1008 can be implemented as multipleapplications 1008 on the computer 1002. In addition, althoughillustrated as internal to the computer 1002, in alternativeimplementations, the application 1008 can be external to the computer1002.

The computer 1002 can also include a power supply 1014. The power supply1014 can include a rechargeable or non-rechargeable battery that can beconfigured to be either user- or non-user-replaceable. In someimplementations, the power supply 1014 can include power-conversion andmanagement circuits, including recharging, standby, and power managementfunctionalities. In some implementations, the power supply 1014 caninclude a power plug to allow the computer 1002 to be plugged into awall socket or a power source to, for example, power the computer 1002or recharge a rechargeable battery.

There can be any number of computers 1002 associated with, or externalto, a computer system containing computer 1002, with each computer 1002communicating over network 1030. Further, the terms “client,” “user,”and other appropriate terminology can be used interchangeably, asappropriate, without departing from the scope of the present disclosure.Moreover, the present disclosure contemplates that many users can useone computer 1002, and one user can use multiple computers 1002.

Implementations of the subject matter and the functional operationsdescribed in this specification can be implemented in digital electroniccircuitry, in tangibly embodied computer software or firmware, incomputer hardware, including the structures disclosed in thisspecification and their structural equivalents, or in combinations ofone or more of them. Software implementations of the described subjectmatter can be implemented as one or more computer programs. Eachcomputer program can include one or more modules of computer programinstructions encoded on a tangible, non-transitory, computer-readablecomputer-storage medium for execution by, or to control the operationof, data processing apparatus. Alternatively, or additionally, theprogram instructions can be encoded in/on an artificially generatedpropagated signal. For example, the signal can be a machine-generatedelectrical, optical, or electromagnetic signal that is generated toencode information for transmission to suitable receiver apparatus forexecution by a data processing apparatus. The computer-storage mediumcan be a machine-readable storage device, a machine-readable storagesubstrate, a random or serial access memory device, or a combination ofcomputer-storage mediums.

The terms “data processing apparatus,” “computer,” and “electroniccomputer device” (or equivalent as understood by one of ordinary skillin the art) refer to data processing hardware. For example, a dataprocessing apparatus can encompass all kinds of apparatuses, devices,and machines for processing data, including by way of example, aprogrammable processor, a computer, or multiple processors or computers.The apparatus can also include special purpose logic circuitryincluding, for example, a central processing unit (CPU), a fieldprogrammable gate array (FPGA), or an application specific integratedcircuit (ASIC). In some implementations, the data processing apparatusor special purpose logic circuitry (or a combination of the dataprocessing apparatus or special purpose logic circuitry) can behardware- or software-based (or a combination of both hardware- andsoftware-based). The apparatus can optionally include code that createsan execution environment for computer programs, for example, code thatconstitutes processor firmware, a protocol stack, a database managementsystem, an operating system, or a combination of execution environments.The present disclosure contemplates the use of data processingapparatuses with or without conventional operating systems, for example,LINUX, UNIX, WINDOWS, MAC OS, ANDROID, or IOS.

A computer program, which can also be referred to or described as aprogram, software, a software application, a module, a software module,a script, or code, can be written in any form of programming language.Programming languages can include, for example, compiled languages,interpreted languages, declarative languages, or procedural languages.Programs can be deployed in any form, including as stand-alone programs,modules, components, subroutines, or units for use in a computingenvironment. A computer program can, but need not, correspond to a filein a file system. A program can be stored in a portion of a file thatholds other programs or data, for example, one or more scripts stored ina markup language document, in a single file dedicated to the program inquestion, or in multiple coordinated files storing one or more modules,sub programs, or portions of code. A computer program can be deployedfor execution on one computer or on multiple computers that are located,for example, at one site or distributed across multiple sites that areinterconnected by a communication network. While portions of theprograms illustrated in the various figures may be shown as individualmodules that implement the various features and functionality throughvarious objects, methods, or processes, the programs can instead includea number of sub-modules, third-party services, components, andlibraries. Conversely, the features and functionality of variouscomponents can be combined into single components as appropriate.Thresholds used to make computational determinations can be statically,dynamically, or both statically and dynamically determined.

The methods, processes, or logic flows described in this specificationcan be performed by one or more programmable computers executing one ormore computer programs to perform functions by operating on input dataand generating output. The methods, processes, or logic flows can alsobe performed by, and apparatus can also be implemented as, specialpurpose logic circuitry, for example, a CPU, an FPGA, or an ASIC.

Computers suitable for the execution of a computer program can be basedon one or more of general and special purpose microprocessors and otherkinds of CPUs. The elements of a computer are a CPU for performing orexecuting instructions and one or more memory devices for storinginstructions and data. Generally, a CPU can receive instructions anddata from (and write data to) a memory. A computer can also include, orbe operatively coupled to, one or more mass storage devices for storingdata. In some implementations, a computer can receive data from, andtransfer data to, the mass storage devices including, for example,magnetic disks, magneto optical disks, or optical disks. Moreover, acomputer can be embedded in another device, for example, a mobiletelephone, a personal digital assistant (PDA), a mobile audio or videoplayer, a game console, a global positioning system (GPS) receiver, or aportable storage device such as a universal serial bus (USB) flashdrive.

Computer readable media (transitory or non-transitory, as appropriate)suitable for storing computer program instructions and data can includeall forms of permanent/non-permanent and volatile/non-volatile memory,media, and memory devices. Computer readable media can include, forexample, semiconductor memory devices such as random access memory(RAM), read only memory (ROM), phase change memory (PRAM), static randomaccess memory (SRAM), dynamic random access memory (DRAM), erasableprogrammable read-only memory (EPROM), electrically erasableprogrammable read-only memory (EEPROM), and flash memory devices.Computer readable media can also include, for example, magnetic devicessuch as tapes, cartridges, cassettes, and internal/removable disks.Computer readable media can also include magneto optical disks andoptical memory devices and technologies including, for example, digitalvideo disc (DVD), CD ROM, DVD+/−R, DVD-RAM, DVD-ROM, HD-DVD, and BLURAY.The memory can store various objects or data, including caches, classes,frameworks, applications, modules, backup data, jobs, web pages, webpage templates, data structures, database tables, repositories, anddynamic information. Types of objects and data stored in memory caninclude parameters, variables, algorithms, instructions, rules,constraints, and references. Additionally, the memory can include logs,policies, security or access data, and reporting files. The processorand the memory can be supplemented by, or incorporated in, specialpurpose logic circuitry.

Implementations of the subject matter described in the presentdisclosure can be implemented on a computer having a display device forproviding interaction with a user, including displaying information to(and receiving input from) the user. Types of display devices caninclude, for example, a cathode ray tube (CRT), a liquid crystal display(LCD), a light-emitting diode (LED), and a plasma monitor. Displaydevices can include a keyboard and pointing devices including, forexample, a mouse, a trackball, or a trackpad. User input can also beprovided to the computer through the use of a touchscreen, such as atablet computer surface with pressure sensitivity or a multi-touchscreen using capacitive or electric sensing. Other kinds of devices canbe used to provide for interaction with a user, including to receiveuser feedback including, for example, sensory feedback including visualfeedback, auditory feedback, or tactile feedback. Input from the usercan be received in the form of acoustic, speech, or tactile input. Inaddition, a computer can interact with a user by sending documents to,and receiving documents from, a device that is used by the user. Forexample, the computer can send web pages to a web browser on a user'sclient device in response to requests received from the web browser.

The term “graphical user interface,” or “GUI,” can be used in thesingular or the plural to describe one or more graphical user interfacesand each of the displays of a particular graphical user interface.Therefore, a GUI can represent any graphical user interface, including,but not limited to, a web browser, a touch screen, or a command lineinterface (CLI) that processes information and efficiently presents theinformation results to the user. In general, a GUI can include aplurality of user interface (UI) elements, some or all associated with aweb browser, such as interactive fields, pull-down lists, and buttons.These and other UI elements can be related to or represent the functionsof the web browser.

Implementations of the subject matter described in this specificationcan be implemented in a computing system that includes a back-endcomponent, for example, as a data server, or that includes a middlewarecomponent, for example, an application server. Moreover, the computingsystem can include a front-end component, for example, a client computerhaving one or both of a graphical user interface or a Web browserthrough which a user can interact with the computer. The components ofthe system can be interconnected by any form or medium of wireline orwireless digital data communication (or a combination of datacommunication) in a communication network. Examples of communicationnetworks include a local area network (LAN), a radio access network(RAN), a metropolitan area network (MAN), a wide area network (WAN),Worldwide Interoperability for Microwave Access (WIMAX), a wirelesslocal area network (WLAN) (for example, using 802.11 a/b/g/n or 802.20or a combination of protocols), all or a portion of the Internet, or anyother communication system or systems at one or more locations (or acombination of communication networks). The network can communicatewith, for example, Internet Protocol (IP) packets, frame relay frames,asynchronous transfer mode (ATM) cells, voice, video, data, or acombination of communication types between network addresses.

The computing system can include clients and servers. A client andserver can generally be remote from each other and can typicallyinteract through a communication network. The relationship of client andserver can arise by virtue of computer programs running on therespective computers and having a client-server relationship.

Cluster file systems can be any file system type accessible frommultiple servers for read and update. Locking or consistency trackingmay not be necessary since the locking of exchange file system can bedone at application layer. Furthermore, Unicode data files can bedifferent from non-Unicode data files.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of what may beclaimed, but rather as descriptions of features that may be specific toparticular implementations. Certain features that are described in thisspecification in the context of separate implementations can also beimplemented, in combination, in a single implementation. Conversely,various features that are described in the context of a singleimplementation can also be implemented in multiple implementations,separately, or in any suitable sub-combination. Moreover, althoughpreviously described features may be described as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can, in some cases, be excised from thecombination, and the claimed combination may be directed to asub-combination or variation of a sub-combination.

Particular implementations of the subject matter have been described.Other implementations, alterations, and permutations of the describedimplementations are within the scope of the following claims as will beapparent to those skilled in the art. While operations are depicted inthe drawings or claims in a particular order, this should not beunderstood as requiring that such operations be performed in theparticular order shown or in sequential order, or that all illustratedoperations be performed (some operations may be considered optional), toachieve desirable results. In certain circumstances, multitasking orparallel processing (or a combination of multitasking and parallelprocessing) may be advantageous and performed as deemed appropriate.

Moreover, the separation or integration of various system modules andcomponents in the previously described implementations should not beunderstood as requiring such separation or integration in allimplementations, and it should be understood that the described programcomponents and systems can generally be integrated together in a singlesoftware product or packaged into multiple software products.

Accordingly, the previously described example implementations do notdefine or constrain the present disclosure. Other changes,substitutions, and alterations are also possible without departing fromthe spirit and scope of the present disclosure.

Furthermore, any claimed implementation is considered to be applicableto at least a computer-implemented method; a non-transitory,computer-readable medium storing computer-readable instructions toperform the computer-implemented method; and a computer systemcomprising a computer memory interoperably coupled with a hardwareprocessor configured to perform the computer-implemented method or theinstructions stored on the non-transitory, computer-readable medium.

A number of embodiments of these systems and methods have beendescribed. Nevertheless, it will be understood that variousmodifications may be made without departing from the spirit and scope ofthis disclosure

We claim:
 1. A method comprising: generating a first time-frequencyspectrum of a first seismic trace from an original seismic dataset;generating a second time-frequency spectrum of a second seismic tracefrom an enhanced seismic dataset, wherein the second seismic tracecorresponds to the first seismic trace; and re-combining an amplitudespectrum of the first time-frequency spectrum and a phase spectrum ofthe second time-frequency spectrum to generate a third time-frequencyspectrum of an output trace that corresponds to the first and secondseismic traces.
 2. The method of claim 1, further comprising: generatinga time-based output trace from the third time-frequency spectrum.
 3. Themethod of claim 2, wherein generating the first time-frequency spectrumcomprises using short-term Fourier transform (STFT) to generate thefirst time-frequency spectrum, and wherein generating the time-basedoutput trace comprises using inverse short-term Fourier transform(ISTFT) to generate the time-based output trace.
 4. The method of claim1, wherein the enhanced seismic dataset is generated by performing asignal-to-noise ratio (SNR) enhancement procedure on the originalseismic dataset.
 5. The method of claim 4, wherein the SNR enhancementprocedure comprises: common-reflection surface method (CRS),multi-focusing (MF), supergrouping, or non-linear beamforming.
 6. Themethod of claim 1, wherein the enhanced seismic dataset has an identicalacquisition geometry to the original seismic dataset, and wherein thesecond seismic trace is located in the same position in the enhancedseismic dataset as the first seismic trace in the original seismicdataset.
 7. The method of claim 1, wherein the original seismic datasetcomprises a plurality of seismic traces, the method further comprising:for each seismic trace of the plurality, generating a respective outputtrace corresponding to the seismic trace, wherein the respective outputtraces collectively form an output seismic dataset.
 8. A devicecomprising: one or more processors; and a non-transitorycomputer-readable storage medium coupled to the one or more processorsand storing programming instructions for execution by the one or moreprocessors, the programming instructions instructing the one or moreprocessors to perform operations comprising: generating a firsttime-frequency spectrum of a first seismic trace from an originalseismic dataset; generating a second time-frequency spectrum of a secondseismic trace from an enhanced seismic dataset, wherein the secondseismic trace corresponds to the first seismic trace; and re-combiningan amplitude spectrum of the first time-frequency spectrum and a phasespectrum of the second time-frequency spectrum to generate a thirdtime-frequency spectrum of an output trace that corresponds to the firstand second seismic traces.
 9. The device of claim 8, the operationsfurther comprising: generating a time-based output trace from the thirdtime-frequency spectrum.
 10. The device of claim 9, wherein generatingthe first time-frequency spectrum comprises using short-term Fouriertransform (STFT) to generate the first time-frequency spectrum, andwherein generating the time-based output trace comprises using inverseshort-term Fourier transform (ISTFT) to generate the time-based outputtrace.
 11. The device of claim 8, wherein the enhanced seismic datasetis generated by performing a signal-to-noise ratio (SNR) enhancementprocedure on the original seismic dataset.
 12. The device of claim 11,wherein the SNR enhancement procedure comprises: common-reflectionsurface method (CRS), multi-focusing (MF), supergrouping, or non-linearbeamforming.
 13. The device of claim 8, wherein the enhanced seismicdataset has an identical acquisition geometry to the original seismicdataset, and wherein the second seismic trace is located in the sameposition in the enhanced seismic dataset as the first seismic trace inthe original seismic dataset.
 14. The device of claim 8, wherein theoriginal seismic dataset comprises a plurality of seismic traces, andwherein the operations further comprise: for each seismic trace of theplurality, generating a respective output trace corresponding to theseismic trace, wherein the respective output traces collectively form anoutput seismic dataset.
 15. A non-transitory computer-readable mediumstoring instructions executable by a computer system to performoperations comprising: generating a first time-frequency spectrum of afirst seismic trace from an original seismic dataset; generating asecond time-frequency spectrum of a second seismic trace from anenhanced seismic dataset, wherein the second seismic trace correspondsto the first seismic trace; and re-combining an amplitude spectrum ofthe first time-frequency spectrum and a phase spectrum of the secondtime-frequency spectrum to generate a third time-frequency spectrum ofan output trace that corresponds to the first and second seismic traces.16. The non-transitory computer-readable medium of claim 15, theoperations further comprising: generating a time-based output trace fromthe third time-frequency spectrum.
 17. The non-transitorycomputer-readable medium of claim 16, wherein generating the firsttime-frequency spectrum comprises using short-term Fourier transform(STFT) to generate the first time-frequency spectrum, and whereingenerating the time-based output trace comprises using inverseshort-term Fourier transform (ISTFT) to generate the time-based outputtrace.
 18. The non-transitory computer-readable medium of claim 15,wherein the enhanced seismic dataset is generated by performing asignal-to-noise ratio (SNR) enhancement procedure on the originalseismic dataset.
 19. The non-transitory computer-readable medium ofclaim 18, wherein the SNR enhancement procedure comprises:common-reflection surface method (CRS), multi-focusing (MF),supergrouping, or non-linear beamforming.
 20. The non-transitorycomputer-readable medium of claim 15, wherein the enhanced seismicdataset has an identical acquisition geometry to the original seismicdataset, and wherein the second seismic trace is located in the sameposition in the enhanced seismic dataset as the first seismic trace inthe original seismic dataset.